I am dealing with a 3x4 complex matrix(adsbygoogle = window.adsbygoogle || []).push({}); Mthat relates a vectordto another vetorc. That is:

c= [M]*dis 4x1 and

dcis 3x1. I want to introduce a new line (constraint) intoM, say d(1) = d(2). However, I would like to only apply the constraint to the real or only the imaginary parts. Is this possible?

Let me rephrase to give some perspective.Mis a complex matrix that represents the frequency response of a system at a given frequency, thusMis complex as each element has magnitude and phase. Since my system has 3 outputs and 4 inputs, I want to introduce a constraint to make my matrix square (and ensure there is only one solution). I know I can set d(1) = d(2) or any relationship like that, but that locks both amplitude and phase of d(1) and d(2) together. Is there any way to set only the amplitudes together, or only the phases together?

Ideally, I'd like to set their amplitudes to a ratio of 1/10 and dont care what their phases to do whatever. This is where I get a bit murky...Is this possible?

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# A Complex Matrix Rank

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